Dynamical analysis of a stochastic prey-predator model with fear effect and feedback control

In this work, the intricacies and complexities of dynamical properties are extensively studied for the proposed deterministic and stochastic prey-predator models. The influence of fear effects, prey refuge and feedback control are considered and thorough theoretical research is conducted on the systems. It commences by establishing the global stability and uniqueness of the positive equilibrium of the deterministic model. Then for the stochastic system, the existence, uniqueness and boundedness of a global positive solution are analysed by constructing appropriate Lyapunov functions. Sufficient conditions are established for the extinction and persistence of the stochastic model. It can be observed that both the fear effect and prey refuge have a greatly impact on the dynamics of system. Intermediate values of feedback control intensity may be the most beneficial to species coexistence. It provides new insights into the sustainability of ecosystems.